Question: Simplify the following expression and state the condition under which the simplification is valid: $q = \dfrac{t^2 + 7t}{t^2 + 4t - 21}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{t^2 + 7t}{t^2 + 4t - 21} = \dfrac{(t)(t + 7)}{(t - 3)(t + 7)} $ Notice that the term $(t + 7)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(t + 7)$ gives: $q = \dfrac{t}{t - 3}$ Since we divided by $(t + 7)$, $t \neq -7$. $q = \dfrac{t}{t - 3}; \space t \neq -7$